Cooperative games model the allocation of profit from joint actions, following considerations such as stability and fairness. We propose the reliability extension of such games, where agents may fail to participate in the game. In the reliability extension, each agent only “survives” with a certain probability, and a coalition’s value is the probability that its surviving members would be a win...

In this paper we discuss Hausdorff and packing measures of random continuous trees called stable trees. Stable trees form a specific class of Lévy trees (introduced by Le Gall and Le Jan in [28]) that contains Aldous’s continuum random tree which corresponds to the Brownian case. We provide results for the whole stable trees and for their level sets that are the sets of points situated at a giv...

The core and the Shapley value are important solution concepts in cooperative game theory. While the core is designed for the stability of the game, the Shapley value aims for fairness among the players. However, the Shapley value might not lie within the core and a core solution might not be ‘fair’. We introduce a new solution concept called the ‘fairest core’, one that aims for both stability...